Related papers: On non-Archimedean and motivic distributions defin…
We develop a theory of local densities and tangent cones in a motivic framework, extending work by Cluckers-Comte-Loeser about $p$-adic local density. We prove some results about geometry of definable sets in Henselian valued fields of…
The concept of wave front set was introduced in 1969-1970 by M. Sato in the hyperfunctions context and by L. H\"ormander in the $\mathcal C^{\infty}$ context. Howe used the theory of wave front sets in the study of Lie groups…
We survey our recent work on an extension of the theory of motivic integration, called arithmetic motivic integration. We developed this theory to understand how p-adic integrals of a very general type depend on p.
We study the scattering of waves in systems with losses or gains simulated by imaginary potentials. This is done for a complex delta potential that corresponds to a spatially localized absorption or amplification. In the Argand plane the…
We introduce from an analytic perspective Christoffel-Darboux kernels associated to bounded, tracial noncommutative distributions. We show that properly normalized traces, respectively norms, of evaluations of such kernels on finite…
A kernel of a directed graph is a subset of vertices that is both independent and absorbing (every vertex not in the kernel has an out-neighbour in the kernel). Not all directed graphs contain kernels, and computing a kernel or deciding…
We study the concentration of random kernel matrices around their mean. We derive nonasymptotic exponential concentration inequalities for Lipschitz kernels assuming that the data points are independent draws from a class of multivariate…
This survey paper, to appear in he proceedings of the Miami Winter School ``Geometric Methods in Algebra and Number Theory'', is concerned with extending classical results \`a la Ax-Kochen-Er{\v{s}}ov to $p$-adic integrals in a motivic…
We deal with kernel theorems for modulation spaces. We completely characterize the continuity of a linear operator on the modulation spaces $M^p$ for every $1\leq p\leq\infty$, by the membership of its kernel to (mixed) modulation spaces.…
We use the theory of motivic integration in order to give a geometric explanation of the behavior of some p-adic integrals.
This article gives an introduction to arithmetic motivic integration in the context of p-adic integrals that arise in representation theory. A special case of the fundamental lemma is interpreted as an identity of Chow motives.
We generalize the motivic incarnation morphism from the theory of arithmetic integration to the relative case, where we work over a base variety S over a field k of characteristic zero. We develop a theory of constructible effective Chow…
This paper is dedicated to the study of the kernel of the "compact motivization" functor $M_{k}^c:SH^c(k)\to DM^c(k)$ (i.e., we try to describe those compact objects of $SH(k)$ whose associated motives vanish. Moreover, we study the…
Consider a setting with multiple units (e.g., individuals, cohorts, geographic locations) and outcomes (e.g., treatments, times, items), where the goal is to learn a multivariate distribution for each unit-outcome entry, such as the…
We study Riesz distributions in the framework of rational Dunkl theory associated with root systems of type A. As an important tool, we employ a Laplace transform involving the associated Dunkl kernel, which essentially goes back to…
We study some constructions on distributions in a uniform $p$-adic context, and also in large positive characteristic, using model theoretic methods. We introduce a class of distributions which we call distributions of ${\mathscr…
In a digraph, a kernel is a subset of vertices that is both independent and absorbing. Kernels have important applications in combinatorics and outside. Kernels do not always exist and finding sufficient conditions ensuring their existence…
The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their…
Sklar's theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of p-boxes,…
This paper reviews the checkered history of predictive distributions in statistics and discusses two developments, one from recent literature and the other new. The first development is bringing predictive distributions into machine…